More attacks will be made against Iran and the militias it arms and funds if Yank forces in the Mideast continue to be targeted, the White House warned Sunday, saying that it nonetheless is not seeking an “open-ended military campaign” across the region.

“We are prepared to deal with anything that any group or any country tries to come at us with,” the national security adviser, Jake Sullivan, said. He added that Iran should expect “a swift and forceful response” if it — and not one of its proxies — “chose to respond directly” against America.

Mr. Sullivan delivered the warnings in interviews with television news shows after America and Britain on Saturday struck 36 Houthi targets in Yemen. The Iran-backed terrorists have fired on American and international interests repeatedly in the wake of Israel’s war to dismantle Hamas.

An air assault Friday in Iraq and Syria targeted other Iranian-backed militias and the Iranian Revolutionary Guard in retaliation for the drone strike that killed three U.S. troops in Jordan last weekend. The U.S. fired again at Houthi targets on Sunday.

“We cannot rule out that there will be future attacks from Iranian-backed militias in Iraq and Syria or from the Houthis,” Mr. Sullivan said. He said the president has told his commanders that “they need to be positioned to respond to further attacks as well.”

Mr. Biden “is not looking for a wider war,” he emphasized when questioned about the potential for strikes inside Iran that would expand the conflict in the volatile region. But when asked about the possibility of direct escalation by the Iranians, Mr. Sullivan said: “If they chose to respond directly to the United States, they would be met with a swift and forceful response from us.”

The White House has blamed the attack at the Tower 22 base in Jordan on January 28 on the Islamic Resistance in Iraq, a coalition of Iranian-backed militias. Iran has flimsily tried to distance itself from the drone strike, saying the militias act independently of its direction.

While pledging to respond in a “sustained way” to new assaults on Americans, Mr. Sullivan said he “would not describe it as some open-ended military campaign.”

Still, he said, “We intend to take additional strikes and additional action to continue to send a clear message that the United States will respond when our forces are attacked or our people are killed.”

There will be more steps taken, he said. “Some of those steps will be seen. Some may not be seen.”

The American strike on dozens of sites in Iraq and Syria hit more than 85 targets at seven locations. These included command and control headquarters, intelligence centers, rockets and missiles, drone and ammunition storage sites, and other facilities that were connected to the militias or the Islamic Revolutionary Guard Corps’ Quds Force, the expeditionary unit that handles Tehran’s relationships with, and arming of, regional militias.

The Biden administration has so far appeared to stop short of directly targeting Iran or senior leaders of the Quds Force within its borders. The U.S. military does not have any confirmation at this time of civilian casualties from those strikes, Mr. Sullivan said. 

“What we do know is that the targets we hit were absolutely valid targets from the point of view of containing the weaponry and the personnel that were attacking American forces. So, we are confident in the targets that we struck.”

The strikes overnight Sunday struck across six provinces of Yemen held by the Houthi rebels, including at Sanaa, the capital. The Houthis gave no assessment of the damage but American officials described hitting underground missile arsenals, launch sites, and helicopters used by the rebels.

A Houthi military spokesman, Brigadier General Yahya Saree, said, “The aggressors’ airstrikes will not go unanswered.”

Meanwhile, Iran warned Washington over potentially targeting two cargo ships in the Mideast long suspected of serving as forwarding operating bases for Iranian commandos. The statement from Iran on the Behshad and Saviz ships appeared to signal Tehran’s growing unease over the American strikes across the region.

The ships are registered as commercial cargo ships with a Tehran-based company the American Treasury has sanctioned as a front for the state-run Islamic Republic of Iran Shipping Lines. The Saviz, then later the Behshad, have loitered for years in the Red Sea off the coast of Yemen, suspected of serving as spy positions for Iran’s Revolutionary Guard.